Question: Find the domain of y=arcsin(x^2) \\ -1 \leq x^2 \leq 1 \\\\ $But we know that $ x^2 \geq 0 $ for all real $ x $ so we can change this inequality to make it $ 0 \leq x^2 \leq 1 \\\\ $We can look at these inequalities separately if you like:$ \\\\ x^2 \geq 0 $ for all real $ x $ so we can 'ignore' this one since it's trivial. $ \\\\ $So we look at the other part, which is $ x^2 \leq 1 \\\\ -1 \leq x \leq 1 \\\\ $And so that is our answer.$